Method and apparatus for electrical exploration of subsurfaces



p 1939. J. J. JAKOSKY 2,174,343

METHOD AND APPARATUS FOR ELECTRICAL EXPLORATION OF SUBSURFACES Filed May 24, 1957 4 Sheets-Sheet 1 ATTORNEYS,

p 1939. J. J. JAKOSKY 2,174,343

METHOD AND APPARATUS FOR ELECTRICAL EXPLORATION 0F SUBSURFACES Filed May 24; 1937 4 Sheets-Sheet 2 p 6, 1939. j J. J. JAKOSKY 2,174,343

METHOD AND APPARATUS FOR ELECTRICAL EXPLORATION OF' SUBSURFACES Filed May 24, 1937 4 Sheets-Sheet 4v JbzzJ' JILWENTEP o ai rvs g, kn/my,

ATTORNEYS Patented Sept. 26, 1939,

UNITED STATES PATENT OFFICE John Jay Jakosky, Los Angeles, Calif.

Application May 24,

9 Claims.

This invention relates to the electrical exploration of the subsurface and pertains more particularly to a method and apparatus for investigating the nature and characteristics of the subsurface to provide a method and apparatus for the electrical exploration of the subsurface which may be utilized without requiring the direct measurement of any conventional electrical quantity such as potential, current, resistivity, or the like, and which preferably involves only the measurement of the ratio between the values, at different points, of a quantity, such as an electrical or magnetic variable, influenced by the angle of penetration of the path of an electrical current through the earth.

Another important object of the invention is to provided a method and apparatus which may be utilized without requiring measurement of the absolute value of energizing current flowing through the earth and in which the obtaining of reliable results is not absolutely dependent upon the accurate maintenance of a constant or predetermined current flow for successive measurements, although for best results the current is maintained substantially constant or is caused to'conform substantially to a regular predetermined relationship, for successive measurements.

A further object of the invention is to provide a method and apparatus for the electrical exploration of the subsurface in which the results obtained, whenusing alternating current or short pulses of unidirectional current, are subsantially free from indeterminate errors resulting from phase differences between the energizing current and the resulting potentials existing at points on the earth between which measurements are taken.

A very important object of this invention is to .provide for minimizing the effects of ground currents. When measurements are made between electrodes spaced a long distance such as 5,000 to 15,000 feet apart, these ground current variations are often from 25 to 500 'millivolts in a few seconds time. Such changes introduce serious 1937, Serial No. 144,467

errors in any type of potential measurement. These ground currents are regional in character and therefore their magnitude is proportional to the separation between the potential electrodes. The short distance or separation between the potential electrodes used in this invention practically eliminates all errors introduced in the measurements by even the most severe natural earth currents.

Another object of the invention is to provide a method and apparatus for the electrical exploration of the subsurface which gives results which are practically independent of current stake resistance.

A further object is to provide a method and apparatus for electrical exploration of the subsurface with which the effects of the near surface inhomogeneities may be definitely ascertained and. differentiated from the deeper lying structural effects of economic importance.

Another object is to provide an electrical method and apparatus for ascertaining the presence, location, and direction and degree of slope, of sloping contacts in the subsurface, and for accurately locating faults and contacts in the subsurface.

Another object of the invention is to provide a method for the electrical exploration of the subsurface in which the electrochemical effects produced by the flow of the energizing current are utilized to an important degree.

Another object of the invention is to provide. a method for the electrical exploration of the subsurface in which the time, density, direction, and electrolytic effects of a flow of current through the earth are correlated.

Further objects and advantages of the invention will either be specifically brought out in the following description or will be apparent therefrom.

According to this invention an electrical current is passed through the earth between a pair of current or energizing electrodes While a measurement is taken adjacent at least one of said electrodes, which is indicative of the angle of penetration of the mean path of the current flowing between said electrodes. In investigating the subsurface structure, the path of the current through the earth between said electrodes is varied, by moving at least one of the electrodes to different positions on the surface of the earth, and the measurement indicative of the angle of penetration is repeated for each position of the electrodes, so as to obtain a series of measurements indicative of the angle of penetration of the current flow for different spacial arrangements of the electrodes. In order to obtain more complete information, the desired measurements are preferably taken adjacent each of the energizing electrodes for each successive position thereof. Certain relations are preferably maintained between time, density, and direction of current flow at the successive electrode positions, in order to correlate the results and allow for the full and diagnostic effects of certain electrochemical'actions produced in the subsurface as a result of the fiow of current.

The angle of penetration of the current into the, earth from an energizing electrode may be determined, for example, by measuring the potential gradient or the magnetic field strength at two or more positions adjacent that electrode, and comparing the measurements so obtained, but I prefer, in general, to measure a" single quantity whose value is directly indicative of the angle of penetration. According to the preferred embodiment of the invention, as hereinafter more specifically disclosed, such a single measurement is obtained by measuring the ratio of two potential difference values, or of two magnetic field strength values, at different positions adjacent the energizing electr de. sults obtained are dependent upon the relative values of the potential gradient or magnetic field strength at two or more positions adjacent the energizing electrode, and therefore refiect inho-' mogeneities in the actual subsurface structure much more accurately and reliably than other methods in which only a single measurement of potential or of magnetic field strength is made for each position of the energizing electrodes. In such single measurement methods, the results are largely, if not predominantly, affected by the near-surface distribution of current flow, due for example, to near-surface layers of relatively high or relatively low resistance, so that the single measurement does not give an accurate indication of variations in the path of current flow below these near-surface layers. 0n the other hand, by taking measurements which refiect the rela-- tive values of. the potential gradient or magnetic field strength at two or more positions adjacent .the energizing electrode, these effects of nearsurface layers are substantially eliminated, and

true indications of the effects of deeper lying structures upon the path of current fiow are obtained.

The apparatus employed may comprise, in general, a plurality of spaced electrodes in electrical contact with the earth and electrically associated with a source of electrical power for passing an electric current through the earth between said electrodes, and means for measuring, adjacent one 7 of said electrodes, a quantity indicative of the ansic of penetration of the current. I preferably also I provide means for taking similar measurements adjacent the other electrode or electrodes. This usually allows for better correlation of'the field data, provides more data, and provides for the positive detection of anomalous near-surface effects. The measuring means may comprise, for example, potentiometric means for measuring the differences of potential at two or more different positions adjacent an energizing electrode, or magnetometric means for measuring the magnetic field strength at two such positions, or

tions, whereby the angle of penetration of the current may be determined by comparison of In either case, the rethe measurements so obtained. In its preferred embodiments, however, the measuring means is 01' a type adapted to give a direct indication of the ratio of potential differences, or of magnetic field strengths, at two positions adjacent an energizing electrode. I also find it important to provide means, either manual or automatic, to control the time and magnitude of current fiow, in/order to produce controlled electrolytic effects in the subsurface so that measurements may be taken at suitable tune intervals.

This invention contemplates the passage of direct or alternating current, or of pulsating currents (for example, as described in my Patent No. 2,015,401), through the earth between the current or energizing electrodes, and the use of any suitable system of measurement, such as either magnetic, electromagnetic, or potential systems, for determining the angle of penetration of the current flowing between the energizing electrodes.

The method of the present invention, and several different types of apparatus and field procedures in accordance therewith, are illustrated in the accompanying drawings and referring thereto:

Fig. 1 is a diagrammatic representation of a section of the earth showing the mean path of current flow between a pair of spaced electrodes;

Fig. 2 is a view corresponding to Fig. 1, in which the electrodes are spaced a greater distance from one another;

Fig. 3 is a view corresponding to Fig. 1, but

showing only one electrode which is assumed to section of the earth, showing the manner in which the increased conductivity of strata traversed by the current flow, due to electrochemical action, distorts the normal path of current flow at successively increasing electrode separations;

Figs. 7 and 8 are diagrammatic plan views illustrating difierent positions at which measurements may be taken, with respect to the positions of the energizing electrodes;

Fig.' 9 is a diagrammatic view of a form of apparatus according to my invention;

Figs. 10 and 11 are diagrammatic representations of alternative apparatus arrangements according to my invention;

Fig. 12 is a diagrammatic representation of apparatus which may be utilized to take electromagnetic measurements;

Figs. 13 and 14 are representative data curves which may be obtained adjacent the respective energizing electrodes, when utilizing any of the apparatus arrangements shown in Figs. 9 to 12;

Figs. 15 and 16 are diagrammatic plan views illustrating the manner in which the energizing electrodes and the measuring electrodes may be moved in taking successive measurements;

.Fig. 17 is a diagrammatic plan view illustrating the taking of measurements at three positions adjacent each energizing electrode; and

Fig. 18 is a diagrammatic plan view illustrating a field layout for making a three-directional survey according to this invention.

The method contemplated by this invention is not concerned with the measurement of electrical resistivity of the earth included between the two electrodes, but with a study and analysis of the lines of current flow between the two electrodes. When two electrodes are placed at the surface of the ground a given distance apart, and a source of potential is connected across the electrodes, current flows from one electrode to' the other electrode. The current does not pass directly along the straight line joining these two points. In fact, a relatively small amount of the current chooses this direct path, and the main current flow actually takes place along curved lines extending into the subsurface. The curved paths of this current flow penetrate to depths equal to and greater than the distance between the electrodes. The behavior of these current paths may be understood when it is recalled that electric currents repel one another, somewhat as two bodies with like electrification repel one another. Each current element thus takes a path that enables it to pass'from one electrode to the other electrode and, at the same time, stay as far as possible from all the other current elements. This mutual repulsion causes a spreading out of the current paths and forces some of the current to penetrate to great depths. An effective portion of the current does not penetrate to depths greater than a certain amount, since in penetrating to these greater depths the path of current flow becomes increasingly longer. This results in an increased resistance of the Path through the earth, and as a result the current chooses a compromised path governed by the electrostatic repulsion on the one hand and the actual earth resistance on the other hand. When dealing with a semi-infinite medium, such as the surface of the earth overlain with the air, a perfect insulator, the curvature of the mean effective path of current flow will vary with the distance between the two electrodes and also with variations in the subsurface. This fundamental factor is the basis of operation for the invention described herein.

The actual earth resistance is a variable and is dependent upon the relative positions and characteristics of the various individual traversed by the current flow. It is also dependent upon the electrochemical characteristics of the individual strata and the time of current flow and current density, since the major portion of the conductivity of the subsurface is a result of electrolytic conduction, as has been borne out in practice. The current is carried by the natural electrolyte which exists in the subsurface and which consists of water solutions of the various soluble mineral salts. Such electrolytes follow the general laws of electrolytic conduction very closely and are modified slightly by the included rocks. Thus, the electrical conductivity increases with ionization, which increases with current and with time of current flow, and also with rising temperature. Interpretation of survey data must therefore take into account the general subsurface distribution of ground waters and their variation in chemical content along with the variations in subsurface temperatures.

Since the earth is considered as an electrolytic conductor, the conductivity thereof is a function of thetime and magnitude of energizing current. This is verified by the fact that if a given cur- I rent is passed between two spaced electrodes in strata sistance and polarization adjacent the electrodes) will usually gradually decrease with time until an equilibrium value is reached. If the current flow between the electrodes is now stopped for a short time and again applied, the initial earth resistance will be higher than when the current flow was stopped, but if the time interval between stopping and starting of current flow is not too long, the resistance will still be somewhat lower than when the current was first applied, and will reach equilibrium in a shorter period of time. It is also reasonable to assume, and field results have verified this assumption, that the electrolytes permeating various strata have different electrochemical characteristics so that when a current is passed through these various strata some of them will have greater or lesser electrolytic conductivities and will reach full conductivity in a shorter or longer period of time. Thus, by controlling the duration and density of the energizing current, and by taking measurements at a given time after the energizing current has begun to flow,.the effects due to the various strata may be differentiated.

For the above reasons, I have found it advantageous to maintain a controlled current flow, as indicated by the reading of an ammeter, and to maintain this flow of current for a definite and preferably uniform period, such as from ten,to twenty seconds, at each location before taking measurements, and to stop the flow of current at the end of this period of time. The current flow is then suspended for a short and also preferably uniform interval, such as from thirty to sixty seconds, during which interval one ormore of the electrodes will be moved to new positions to provide new spacial relations thereof. The current flow is then" resumed at the end of this interval of time, and measurements are again taken as before. These time intervals may be varied widely for different surveys, dependent upon the subsurface conditions and the distance between the electrodes and other factors; however, I find it extremely advantageous to maintain a given set of time intervals for any particular survey.

Referring to Fig. 1, two energizing electrodes E1 and E2 are shown connected to a current source S and in electrical contact with the earth at two points spaced a relatively short distance apart in a direction along the surface of the earth. Due to the relatively small distance between the two electrodes, the mean effective path of current flow, as indicated for example at I1, remains relatively near the surface. At some certain distance d from the electrode E1, but adjacent thereto, the current path will make an angle (11 with the earth's surface. If the electrodes E1 and E2 are spaced farther apart, as illustrated in Fig. 2, the current paths, due to the abovementioned mutual repulsion and resistivity effects, will tend to travel downward at a sharper angle. The angle a2 between the mean path of current flow and the earth's surface, at the same distance d from electrode E1, is greater than with the smaller separation of the electrodes as shown in Fig. 1, due not only to the change in shape of the current path curve, but also due to the de' creased relative value of d as compared to the total electrode separation. If the distance between the electrodes E1 and E2 be assumed to approach an infinite distance, then the angle a would approach 90; i. e., the path of current flow, at a position adjacent one of the electrodes.

' the larger electrode spacings, as illustrated in Figs. 1 and 2., Any electrical inhomogeneity in the subsurface will therefore show up by causing deviations of this normal angular increase.

I have illustrated idealized equipotential surfaces existing adjacent electrode E1 in both Figs. 1 and 2, and it may be seen from inspection that as the angle a increases, these-idealized surfaces become more nearly hemispherical and less crowded on the side of electrode E1 toward the other electrode, or, in other words, the potential gradient adjacent the electrode is greater on that side than on the other side, and the difference in potential gradient is greater in Fig. 1 than in Fig. 2.

The shape of these equipotential surfaces is also influenced by variations in the electrical characteristics of the strata at different depths, as is illustrated in Fig. 3, in which the energizing electrode E1 is assumed to be placed at an infinite distance from the other energizing electrode, so that the mean path of current flow from electrode E1 is perpendicular to the surface as indicated at 13. The equipotential theory which has formed the basis of previous methods depends upon the assumption that a point of the surface at a given distance from one of the energizing electrodes has the same potential as all points below the surface at the same distance from said electrode, 1. e., that the points of equal potential around an energizing electrode lie upon a portion of a spherical surface about said electrode, as indicated by semi-circular lines b and c in Fig. 3. On this basis, it has been assumed that anomalies in observed potential values at given distances along the surface from an energizing electrode represent anomalies in the subsurface at that same distance below the surface. This theory would be satisfactory if the earthwere a homogeneous medium. In practice, however, the earth is not homogeneous, and in any given area there is a change in the resistivity with depth. This results in a distortion of the equipotential surfaces. As an illustration, lines b and c' in Fig. 3 represent equipotential surfaces which may actually exist where the earth resistivity decreases with depth. Interpretation based on the equipotential theory will therefore be greatly in error, since the potential at a point on the surface is equal to that of points below the surface at a depth materially less than the distance of said surface point from the energizing electrode.

In order to illustrate the changes in the mean path of current flow under various subsurface conditions with a given finite electrode separa tion, I have illustrated in Figs. 4 and 5 the path of the current adjacent an electrode E1, for two different subsurface conditions, said electrode being in each case spaced from another electrode by the same distance, for example, as shown between El and E: in mg. 1. Let it be assumed that Fig. 1 shows thepath of the current through a homogeneous medium, making an angle :11 with the surface at a given distance from the electrode E1. It will be noted that the equipotential shells drawn about the electrode E1 are crowded closer together on the side toward the other electrode.

7 In 4 the subsurface is assumed to become less resistant with depth and as a consequence the current will tend to penetrate more deeply and make an angle as with the surface which is greater than the angle m in Fig. 1. In this instance the idealized equipotential shells drawn around the electrode E1 are considerably distorted and tend to become flattened. In general, however, the potential gradient at the two sides of the electrode will be more nearly equal than in Fig. 1. In Fig. 5 the subsurface is assumed to become more resistant with depth. As a consequence the mean path of current lies closer to the surface and the angle or is less than the angle (11 in Fig. l. The idealized equipotential shells drawn about the electrode E1 are more distorted than in Fig. 1 and the difference between the potential gradient at the two sides of the electrode is greater than in Fig. l.

I have found, however, that in stratified areas the angle of penetration does not usually vary uniformly with the separation between the energizing electrodes, but increases irregularly as the current begins to penetrate deeper lying conductive strata as the electrode separation is increased or, conversely, decreases irregularly as the current ceases to penetrate the more deeply lying conductive strata as the electrode separation is decreased. In some instances, for example when the electrode spacing is increased, the angle of penetration may actually decrease. This is no doubt due to the fact that the flow of current has produced an increased electrolytic conductivity in the strata traversed thereby to such an extent that when the electrode spacing is subsequently increased the current tends to run along near the surface to the path of such increased conductivity, and flow principally along this path through the earth. Finally, when the electrode spacing has been sufficiently increased, the nearsurface path to the previously established path of reduced resistance will become sufficiently highly resistant so that a significant portion of the current will flow downwardly from the electrodes and establish a new path through a more deeply lying stratum of relatively low resistance. This phenomenon is extremely useful in structure mapping since it gives sharper and' more abrupt indications of changes in the angle of current flow due to the shifting of the main path of current flow from one stratum to another.

I have diagrammatically illustrated this condition in Fig. 6 in which the progressive positions of the electrode E1 are indicated consecutively from 6| to 65. When the electrode E1 is located at El the current flows downwardly and thence through a stratum or zone of high conductivity, such as indicated at 58, making an angle as with the surface of the earth. The flow of current along the path indicated at 66 serves to increase the electrolytic conductivity of the earth in this path. When the electrode is moved to 62 and the current is again applied, the current tends to flow downwardly at an angle as which is less than the angle as, in order to reach the former path 66 of increased conductivity. The same condition is assumed to hold true when the electrode E1 is moved to the point 63 and the current makes an angle of penetration m with the surface of the earth which is again less than the angle (15, and tends to join the old path 86. Upon moving the electrode to the point 64,

the resistance of the path from the point 64 to the old path 66 becomes so high that it is easier for the current to find a new path 61 passing through another highly conductive layer indicated at G9 which lies below the layer indicated at 68. The current will therefore follow principally this new path 61, making an angle as with the surface of the earth. Upon placing the electrode at the current tends to flow near the surface until joining the newly established path 61, making an angle as with the surface. It will of course be appreciated that the above illustration is perhaps somewhat exaggerated in order to more clearly bring out the subsurface conditions which I have found to exist.

Previously proposed methods have not ordinarily been able to detect the variations in the angle of current flow due to the various phenomena described above, since measurements have usually been taken in the region intermediate, and substantially centrally between, the .two electrodes, where these variations in the angle of current flow are not manifested in a particularly pronounced manner, or, stated in a different manner, the measurements have beentaken where the potential curves are relatively flat, and not' affected by the changes in angle of currentflow adjacent the energizing electrodes. Unless measurements are made relatively close to the energizing electrode, the changes in the angle of current flow will be masked by near-surface effects and lateral variations in current flow. The latter two effects increase in importance as the distance from the electrode increases, while the changes in angle of current flow decrease in importance as the distance increases.

The method of this invention is particularly advantageous in detecting the angle of current penetration and variations therein, in that measurements are preferably taken adjacent one or more of the energizing electrodes where the curve of potential drop produced by the flow of current through the earth is much steeper than in the central portion of the spacing between the electrodes. I have found that the sharpest'indications are obtained when measurements are taken at positions adjacent one or more of the energizing electrodes and spaced therefrom by a distance on the order of one-quarter or less of the total separation between the energizing electrodes.

The above considerations explain various ap parent anomalies, such as wide differences in' data taken at the same positions after different time intervals of current flow, and also show that data should be obtained closely adjacent the energizing electrodes, that is, within, for example, a distance in the neighborhood of one-quarter of the distance between energizing electrodes or less,

so that the angle of penetrationof the current flowing between the energizing electrodes, adjacent one or both of the energizing electrodes, may be determined. Thus, by determining the angle of penetration of the current, especially with a control of the time of current flow and of the duration and magnitude of current flow before measurement is taken, deep structural investigations having accuracies equal to or greater than seismic investigations may be 'made. It Will be apparent that .polarization immediately adjacent the energizing electrodes will not affect measurement of the angle of current flow.

In Figs. '7 and 8 I have illustrated diagrammatically certain positions at which measurements may be taken adjacent each of the energizing electrodes E1 and'Ez. As shown in Fig. '7, such measurements may be taken at positions such as indicated at l and 2, adjacent electrode E1 and at positions 3 and 4, adjacent electrode E2.

The positions I, 2, 3, and 4 all lie between the two electrodes and substantially upon a straight line AA on the earths surface, passing through said electrodes. An alternative arrangement is shown in Fig. 8, in which measurements are made at positions 5 and 6 adjacent and at opposite sides of electrode E1, andat positions I and 8 adjacent and at opposite sides of electrode E2, all of said positions 5, 6, l, and 8 again lying upon the straight line A--A passing through the two energizing electrodes It will be seen that, in each case, the two positions of measurement adjacent each electrode are disposed at different relative positions with respect to a plane passing through that electrode and perpendicular to the straight line A--A between said electrodes, so that the relative values of potential or of magnetic field strength at the respective positions will be influenced by, and indicative of, variations in the angle of penetration of the current into the earth. For reasons explained above, the positions of measurement adjacent each electrode (for example, positions I and 2, or positions 5 and 6, adjacent electrode E1) are relatively close to that electrode as compared to the total distance between the two electrodes, and are preferably spaced from that electrode by a distance on the order of one-quarter or less of said total distance.

If the earth traversed by the current flow is homogeneousbetween the electrodes E and E2 the ratio of the potentials existing, for example, at positions 5 and-6 in Fig. 8, may be predicted according to known methods of calculation. Thus by comparing the ratio of potentials existing at 5 and 6 with that which would exist in a homogeneous medium, anomalous deviations in the nature of the subsurface may be determined. In order to compare or determine the potentials existing at 5 and 6 it is convenient to utilize a point of reference'potential located on the surface of the earth. Such a point may be located adjacent the electrode E1, or may be the electrode E1, or it may be at a point sufficiently distant from the electrode E1 to be unaflected by the passage of current through the earth. However, I prefer to utilize a reference potential point adjacent one of the energizing electrodes for measurements which are taken around that particular energizing electrode. For example, in Fig. 8, When measuring around E1, I preferably utilize a point adjacent the electrode E1 located between the electrodes 5 and 6, and sufficiently removed from E1 to be substantially unaffected by the contact potential drop at that electrode. 1

' Such reference potential electrodes are located closely adjacent the respective current electrodes, for example in the neighborhood of five to fifty feet therefrom, and may be located on a line joining the current electrodes or to one side or the other of this line. Since this auxiliary electrode is used for potential measurements only, it is not necessary that it be of size comparable to a current electrode or that it be driven as far into the ground especially when using a voltageoperated device, since electrode resistance will not affect the results. Thus it may be readily transported and easily placed and removed. For example, the auxiliary potential electrode may be fastened to the end of a measuring insulating rod or a flexible non-elastic insulating cord of any convenient length, say five to fifty feet. Thus the auxiliary potential electrode may be easily spaced from the current electrode, at each new location, by the length of the rod or cord, as will be apparent. 1

In order to simplify the description of the drawings, the potentials of the points and 8, for example, are referred to. the potential of the reference potential electrode of that set of electrodes, and the expressions V5 and Va designate the potential at points 5 and 6 with respect to the reference potential electrode. For instance, 11' -the potential ratio at a certain electrode separation in a homogeneous medium is calculated to be -1.150 while the observed ratio is found to be 1.173, then the anomaly would be .023, indicating that some subsurface condition is causing the current to flow downwardly at a smaller angle of penetration than would be normal for that particular electrode separation. The electrode E: may then be moved along the line AA and the ratios'of the potentials existing at 5 and 6 may be taken for various positions of the electrode E2. The theoretical ratio of the potentials existing at 6 and 6 may be calculated for each of the positions of the electrode E2 and subtracted from the actual value of the ratio obtained at each of these points. A curve may then be plotted of the value of the anomaly existing at each of the positions of the electrode E: against the separations of the electrodes E1 and E3. It will be appreciated that the electrode E1 may remain fixed while electrode E1 and the points 5 and 8 are moved as a unit to obtain measurements at different separations of the electrodes E1 and E2, or both electrodes E1 and E2 may be moved outwardly or inwardly along the line A--A. It should also be noted that the electrode E1 need not be equally spaced from the points 5 and 6 and that various spacings may be used throughout a series of measurements without departing from the scope of this invention. However, I prefer to maintain a fixed potential electrode spacing and to take measurements adjacent each of the energizing electrodes for each new spacial arrangement of said electrodes. This allows for better correlation of measurements and for the positive differentiation of anomalous near-surface en'ects and deep structural effects.

An advantageous form of apparatus for obtain- 'Fig. 8. As previously mentioned, various electrode configurations and spacings may be employed, although I prefer to utilize a given configuration with a fixed potential electrode scpa-' ration for a complete series of measurements in order to simplify results. A reference potential electrode P3 is shown adjacent the electrode E1. According to the preferred practice, it will be understood that another set of potential electrodes and a reference electrode will be located adjacent E2, andsimilarly spaced witliigrespect thereto so that ratio measurements may be takenfmdiacent both E1 and E2.

. ;gr grid or input circuits of two vacuum tubes It 2lla'nd'l2 are connected to electrodes P1 and P:

Adjacent E1 are two additional electrodes respectively. The plates of the tubes are connected to a voltage divider l3, across which a galvanometer I4 is connected. Any change in the plate current of either tube may be compensated for by adjusting divider I3 until the galvanometer again indicates a balance. By means of switch IS, the grids of the tubes are biased to limit the plate current to any desired value. The tubes are biased negative to such a value that the plate current'does not exceed the safe operating value of the tubes employed. To compensate for variations in the tubes and sporadic potentials, caused by thermal and chemical effects and ground currents between electrodes P1 and P2, a separate bias control It is inserted in the grid circuit of one of the tubes. This is a form of vacuum tube ratio bridge and is essentially a voltage-operated device. Its operation is {not affected by high circuit resistances, which allows use of a small and conveniently handled reference potential electrode.

Operation of this apparatus is as follows:

Switch I5 is thrown to'zero grid bias, and the V voltage divider ll placed at the midpoint or balance position by throwing switch I! to the right. The bias I6 is now adjusted to bring the galvanometer H to zero balance. This step compensates for all tube and potential variations. The switch [5 is now adjusted to give proper bias to limit the plate current of both tubes when power is applied as indicated by ammeter [8. Since the tubes are biased negatively, an excess bias does no harm and merely decreases the plate current to a minimum value. The switch I! is then thrown to the left and the ratio of the currents flowing through II and I! when current is flowing between E1 and E2 may be determined by the position of the variable tap l9 when the galvanometer I4 is at null position, as will be brought out hereinafter.

When current flows between E1 and E: a ,potential drop occurs between P: and P1, and between Prand P2. The two potentials will, in

general, be unequal. the inequality being'a function of angle of penetration of the current flow, and consequently will be dependent upon the current electrode separation and the subsurface structure. The difference in potentials applied to the grids of the tubes II and I2 will cause a corresponding difference in the plate currents of the two tubes. The arm I! is now adjusted until the galvanometer ll reads zero. By proper calibration, the position of the tap l9 can be made to indicate directly the ratio of the potential difierence between P: and P1 to the potential diifefience between P: and P2. This ratio is now subt acted from the ratio obtained at the same electrode spacing in a theoretically homogeneous medium, and the 1 difference will'represent a anomaly. This procedure is repeated for various current electrode spacings, usually progressively increasing, until the necessary electrode separation has been reached to give the desired depth of penetration. The anomalies may then be plotted versus depth or electrode separation. A plus anomaly indicates that the potential ratio is greater than it should be for a homogeneous medium, which may be accounted for. by one or both of the following conditions: (1) the resistance of the subsurface increases with depth, or (2) an anomalous condition exists in the vicinity'of the electrode system.

The same or comparable apparatus is preferably utilized adjacent the electrode E: so that comparable ratio measurements may be made adjacent that electrode" and compared with the measurements made adjacent E1. A series of such measurements may be made for a number of different positions of the electrodes E1 and E2. For example, the spacing between the electrodes E1 and E2 may be varied by varying the-position of either one or both of the electrodes along a straight line in a 1 given horizontal direction. Numerous arrangements may be utilized for changing the positions of the energizing electrodes, as will be brought out subsequently.

Other voltage-operated devices may be employed for measuring the ratio of potentials, or current-operated devices may be used for measuring this ratio if proper corrections are made for electrode and circuit resistances.

The ratio readings thus obtained at one or both of the energizing electrodes are not ordinarily dependent upon the absolute value of the current flowing between E1 and E2 or uponthe contact resistance of E1 and E2. However, since the resistivity of the earth materials varies with the density of current, it is generally advantageous to make all measurements at a substan-.

tially constant value of the current, for the successive electrode positions, in order to obtain a constant potential drop within the zone of measurement surrounding each energizing. electrode. This constitutes an important feature of the invention, and allows more accurate results than would be possible if any convenient and variable value of current were employed as is done in the conventional resistivity or potential methods hertofore practiced. As an alternative, the current at the successive electrode positions may be varied so as to conform substantially to a regular predetermined relationship, for example, in such manner as to maintain approximately a constant density of current flow through the earth.

In order to simplify the correlation of data obtained at various electrode separations I find it advantageous to maintain the separation of the potential electrodes of each set constant and .at a fixed destance from the adjacent current electrode. That is, the distances E1--P1, E1-P2, E1Pa, P1--Pa and P2--P3 are preferably each maintained constant throughout a series of successive measurements with different spacial relationships of the electrodes E1 and E2. It is not necessary, however, to maintain these conditions, since. the theoretical ratio of potential may be calculated for any given electrode separation.

In Fig. 10 I have shown an apparatus arrangement which is somewhat comparable to that described above. The electrodes E1 and E2 are connected to the surface of the earth and to a source of power S, and potential electrodes P1 and P2 are connected to the earth and to the respective ends of a fixed resistor IIII of sufiiciently. high resistance to prevent distortion of the earth potentials and errors due to contact drops. Electrodes P1 and P2 are spaced from the electrode E1 by the distances d1 and d2 respectively, in, a direction toward electrode E2, and a third potential electrode P3 is located between the electrodes P1 and P2 and spaced from the electrode E1 by distance d2. Although any desired spacing may be utilized between the respective electrodes, I preferably place the electrode P3 midway. between P1 and P2, and the shifting of the electrodes between successive measurements may be facilitated by making the distances P1--P3 and P2--Ps ach equal to the distance P1E1. I also find it preferable to make the distance d: not more than onemeasurements.

fourth the distance between the electrodes E1 and E2, and preferably less.

When current is passed between E1 and E2 there will be a potential drop between P1 and P2 which is greater than the drop between P1 and P2, and by connecting the electrode P3 through amplifier provided with a suitable indicating instrument, to indicate zero potential difference between I03 and P3. This position will be a func-- tion of the ratio of the potentials existing between the three potential electrodes. It will also be obvious that the relative potentials existing at P1, P2, and Pa for any given medium will be a function of the distances d1, d2, and s so that the position of the variable tap I03 for a null reading on the galvanometer I02 will be the same irrespective of the current flow betweenE1 and E2, neglecting the effects of current density upon the electrolytic conductivity of the subsurface. It will be understood that the measuring circuit shown in Fig. 9 may be employed with the elec- 1 trode arrangement shown in Fig. 10, by connecting electrode P1 in Fig. 10 to terminal B of Fig. 9 and connecting electrodes Pa and P2 in Fig.- 10 to terminals A and C in Fig. 9-

A point adjacent one of the energizing electrodes need not be used as a common point of reference potential for taking measurements to determine the angle of penetration of the current flow, as may be demonstrated by referring to Fig. 11. Electrodes E1 and E2 are shown connected to the surface of the earth, and pairs of potential electrodes 'II and I2, and I3 and I4 are located on opposite sides of electrode E1 along the line E1--E2 and are respectively connected to the grid-filament circuits of triodes I5 and I6. The respective plate circuits of the triof the angle of penetration of the current flowing from the electrode E1; As before'pointed out, I preferably take similar readings adjacent the electrode E2 in order to detect anomalies which are caused by near-surface effects. I

The method of this invention is not limited to the employment of potential measurements, and

magnetic measurements may be alternatively" employed. Referring to Fig. 12' I have shown a diagrammatic plan view of a field layout which may be used while taking electromagnetic ratio Energizing electrodes E1 and E2 are connected to the earth and. to a suitable energizing source S, and a pair of coils 26 and 21' The coils 26 and 21 are connected in series with each other and with a resistor 28 to form a closed circuit, and a galvanometer 28 is bridged across this circuit between the coils 26 and 21 and connected to the resistor 28 by a variable tap 36. their axes horizontal and at right angles to the line A-A so that when an alternating current is passed through the earth between El and E2 the magnetic field set up thereby will induce voltages in the coils 26 and 21. It will be apparent that if the coils 26 and 21 have identical characteristics the ratios of the voltages induced therein will be a function of the magnetic potentials existing at 26 and 21 and the relative values thereof may be determined by the position of the tap 30 when a null reading is obtained on the galvanometer 28.

It may be advantageous to employ a unidirectional pulsating current for deep structural investigations, and a slight modification of the apparatus shown in Fig, 12 may be beneficial. For example, the tap 38 may be fixed at the center of the resistor 28, and a ballistic galvanometer may be substituted for the null type of galvanometer 29. The ratio of the magnetic fields existing at 26 and 21 and consequently the angle of penetration of the path of current adjacent the electrode Ez may be readily determined from the galvanometer readings and the circuit characteristics.

In the event that direct current is used to energize the earth, the coils 26 and 21 are preferably rotated at a constant rate and are connected in opposition so as to eliminate the effect of the earth's magnetic field. The planes of the coils 26 and 21 may be vertical, and the coils may be rotated about an axis of rotation which is vertical, so as to cut the horizontal lines of magnetic force. Further simplification of the galvanometer equipment may be obtained by commutating the current according to existing practices. 4

It will be appreciated that numerous procedures may be employed for varying the special relationship of the current electrodes, in determining the sub-surface distribution of current flow. For example, one current electrode may remain fixed, and magnetic or potential ratio measurements may be taken around it asthe other current electrode is moved to positions at different angular directions with respect to said one electrode. The moving current electrode may be moved angularly about a fixed current electrode either with a fixed radius or with a variable radius depending upon whether the survey is of a constant or variable depth. The moving current electrode may be moved along a line in a given horizontal direction to a number of different positions while measurements are taken adjacent the fixed current electrode. While using thisprocedure the survey would be carried to greater depths as the spacing between the electrodes is increased. It will also be appreciated that both of the current electrodes may be moved outwardly or inwardly:

from one another along a given line and that measurements may be taken adjacent either one or both of the electrodes at the different electrode separations.

I may also employ a mobile electrt ie device adapted to .maintain continuous electrical control with the earth, as described in my copending application Serial No. 112,747, filed November 25, 1936, issued as U. S. Patent No. 2,105,247. In some instances where it is desired to make lateral studies, it may be advantageous to move the pair of current electrodes The coils are preferably arranged withwith their associated measuring points to different locations over an area while maintaining the spacing between the current electrodes at a constant value. In any event I find it advantageous to take either the potential or magnetic measurements on a line joining two current electrodes except when measurements are taken in three directions as described below in connection with Figs. 17 and 18.

In Figs. 13 and 14 I have shown a set of curves taken adjacent the electrodes E1 and E: in which the separation of the energizing electrodes is ,plotted against the ratio'anomaly observed adjacent the respective electrodes. The ratio anomaly may be obtained by subtracting the theoretical ratio from the actual ratio obtained and is an index of deviations in the angle of penetration of the current adjacent the respective electrodes. Referring to Fig. 13, the curve 85 is shown with a number of decided inflection points such as 86, 81, 88, 88, 80, and SI, which correspond to separations of the electrodes indicated at 86a to 9la. In Fig. 14 the curve for the electrode E: is indicated at 85' and it will be noted that the inflection points 86 to 9| correspond in general to the points 86 to 9| in Fig. 21, except that they are not quite as well defined. It will also be noted that there are numerous minor inflection points such as 92 and 93 which are present only on the curve 85'. These lastnamed inflection points are no doubt due to nearsurface anomalies in the area traversed by electrode E2, which affect only the measurements taken adjacent that electrode, and since they have no comparable effect on the electrode E1 they bear no relation to the nature of the deep surface structure. The major inflection points which occur on both curves at the same separations are indicative of the nature of the deep structure and show inflection points which are sharper than those exhibited by any electrical exploration method hitherto suggested.

When employing present alternating current methods elaborate precautions must be taken to eliminate phase shift errors in measurements, especially in the case of potential measurements. Although these theoretical precautions may be taken, the practical results are ordinarily not without error because of unknown andvariable phase shift factors which enter into the measurements. Phase shift errors usually increase with the distance over which measurements are taken. By taking ratio measurements between points which are relatively closely spaced, the errors due to phase difference will be negligible. For example, the points 5 and 6 in Fig. 8 may be separated by a few hundred feet or less, while the electrodes E1 and E2 may be separated by several thousand feet. Thus, the phase difference would be negligible at points 5 and 6 due to their proximity; furthermore, ratio measurements are taken and for any given fixed spacing of the measuring points the effects of phase shift on the two potential values will be approximately the same, and will not affect the measured ratio. Also, since natural earth currents are usually regional in character, the potential differences between spaced points, due to such currents, vary with the distance between such points, and by taking measurements between points which are separated by relatively short distances I am able to substantially minimize the errors due to such natural earth potentials.

In Fig. 15 I have illustrated an advantageous form of field procedurejwhich may be used when taking measurements on both sides of the energizing electrodes. When asurvey is to be conducted, for example, to a depth of from 2,000 to 5,000 feet, readings are usually taken withthe energizing electrodes disposed successively at different positions along a line such as B--B, at intervals of, say, 50 feet, with the two energizing electrodes spaced progressively from 6,000 to 15,000 feet. A preliminary surveymay be run along the line B-,-B, and points 4| .and 4| may be located approximately 6,000 feet apart with points 42, 43, 44, 45, and 46 located outwardly from point 4| at desired constant intervals, usually varyingfrom 50 to 500 feet in different surveys, and similar points 42' to 46 located in the same manner with respect to the point 4|. Electrodes D, E, andF may be driven into the ground at 4|, 42, and 43, and electrode E located at the point 42 may be connected through a suitable conductor to a source of power S. Electrodes D and F may be connected to a-suitable ratio measuring device R, such as that shown, for example, in Fig. 9, and an electrode G closely adjacent the electrode E may be connected to the third terminal of ratio, measuring device R. Similar connections may be made .at the points 4|, 42', and 43' to another ratiomeasuring device R'. [I'heelebtrode G which is'used as a source ,of reference potential may comprise a small rod which, may be. thrust into' the. ground and 1 removed, without dimculty.

- After suit ble measurerr'ie tshave been, made at v- 11.'. and R with the arrangement. shown in F 5 1 h e im ND. ma be .1 m ve r m a h oun an lac m o cn ath P in :4 a ec nne'etiq 9 hee e E an F may; be madeso; the electrode F (at point). now I is 1 connected to; the source cf power and electrodes E and D; tat points 42 and). are cone e t ma e-i s d v e 1B. a s m la connections may ,be made at the measuring device R'. The reference electrodeGis removed from itsp osition adjacent the point 42 and inserted in the ground adjacent .the point 43. After measurements have been made at this position the electrode E may be moved forward to the point and the electrode G may be moved adjacent the point 44; this constant progression being maintained throughout the series of measurements.

It will be seen that a survey may be carried out with a minimum amount of work since only one current stake of 'suflicie'ntly large contact surface to be utilized as an energizing electrode must be removed from the ground and driven in again for eachnew position of the energizing electrode, for each set of electrodes. The movement of the reference electrode G does not present any particular difficulty since "it is only a potential electrode and need not be as large as the current stakes. It does not have to be driven as far into the ground and may be removed from the ground with very little effort. This arrangement of electrodes which utilizes a constant spacing has, considerable advantage over. the conventional systems which maintain a constant ratio spacing between the current and energizing electrodes and require the driving of a complete new set of current andpotential stakes for each new.

value of current electrode spacing. -It is also of advantage in that the results are more readily interpreted since the inflection points on the data curves are more pronounced when the potent'ial electrodes are maintained ata small and constant distance from the energizing electrodes.

located at point 43 in Fig. 16 is connected. to one side of the source of power S, and electrodes D and F are located at the points 42 and 4| and are connected to the ratio measuring device. R, and the reference electrode G is located adjacent the electrode E and is connected to the ratio measuring device R, which may, for example, be

of the type shown in Fig. 10. The subsequent movements of electrodes E, F, and D and electrode G are progressive and as outlined for the configuration shown in Fig. 15. It will be noted that the movement of only one current stake is required for each new position of the energizing electrode andthat the reference electrode G is moved in each instance to a point closely adjacent the energizing electrode. This system exhibits the same economies in field procedure as outlined in Fig. 15 and also shows comparable advantages in interpretation of data.

The ratiomeasurements above described have all been taken substantially on a line passing through the current electrodes. Each set of ratio measurements taken adjacent the respective current electrodes will be indicative .of the angle of. penetration of the electrical current flowing throughthe earth adjacent such. current u elect a wit sp c m -wrist c he art Surveys conducted under such conditions will in general indicate vthe. ,presence of: subsurface inhomogeneities. .I-Iowever, there will in generali be, no indication as to the lateral displacement of such inhomogeneities with respect to the line passing through the current electrodes- It will be appreciated that the lateral displacement given traverse over which the inhomogeneities were first noted. However, by utilizing three potential electrodes adjacent an energizing electrode and spaced at different angular directions with respect to said energizing electrode, I have found that I am able to determine'the direction of penetration of the energizing current in three dimensions, that is, to determine not only the angle of penetration with respect to the surface "of the earth, but also the angular deviation of the mean path of current flow with respect to a vertical plane through the two energizing electrodes, and am thus able to determine the lateral displacement of subsurface inhomogeneities.

An arrangement for showing such lateral dis.- placement is diagrammatically illustrated in Fig.

1'7, in which energizing electrodes E1 and E2 are shown connected to the earth and lying on a line A-A. Potential electrodes P7, P8, and P9 are arranged about the electrode E1 and preferably spaced 120 from each other, and poten .tial electrodes P10, P11, and P12 are arranged about the electrode E2 and preferably spaced 120 dimensional direction of penetration of the current flowing between E1 and E2 may be determined. An alternative method consists in comparing the potential between P7 and P3 with the potential between Pa and P9 and between P9 and P7. Knowingthese ratios, the three-dimensional path of current flow may be ascertained.

In Fig. 18 I have shown an electrode arrangement wherebythe dip and strike of strata in an area may be determined with'a single series of measurements without correlation with different distant stations. The clip and strike of the strata in the subsurface below the point and the surrounding area may be determined by surveying three lines, separated by 120, for example, outwardly from the point 5| as at X, Y, and Z. Points 52, 52', and 52 may be located at a given distance from the point 5| on the lines X, Y, and Z respectively, and points 53, 54,55, and 56 may be laid out on the line X at equal intervals outwardly from the point 52. Similar points 53f to 55 and 53" to 56 may be laid out on the lines Y and Z, outwardly of the points 52 and 52 respectively. Electrodes may be driven into the earth at three adjacent points such as 53, 54, and 55 on the line X and at corresponding points on the lines Y and Z, and ratio measuring devices R, R, and R" comparable to that shown in Fig. 9, for example, may be connected to the points 53 and 55 and to a grounded reference electrode G adjacentthe point 54. Theratio measuring. devices R and R may be similarly connected along'the respective lines Y and Z. I preferably provide a switching panel 58 whereby an operator may successively connect a source of power S between the points 54 and 54', 54 and 54", and 54' and 54" so that ratio measurements may be taken successively at R and R, R and R", and R. and R". The energizing points may then be successively moved outwardly to the points 55, 56, etc., on line X, and the corresponding points on Yand Z, and a series of measurements may be taken along the lines X, Y, and Z at each of the new electrode'positions, in a manner comparable to that above described in connection with movement of the electrodes outwardly along a straight line.

It will be obvious that the data taken in the three directions will give the respective angles of current penetration in the three directions, which may be correlated through simple geometric relations to give the dip and strike of the strata adjacent the point 5|. Correlation of this data to obtain the dip and strike is described in my copending application Serial No. 12,640.

It will also be appreciated that other electrode arrangements may be utilized and. that the system of magnetic measurement illustrated in Fig. 12 may be successfully employed for taking the measurements in three directions, in the manner shown in either Fig. 17 or Fig. 18.

I claim:

1. A method of determining the geological nature and characteristics of the subsurface, which comprises: passing an electric current in a path/- the surface of the earth; changing the spacial arrangement of said electrodes and passing ourrent therebetween at different spacial arrangements thereof so as to vary the angle of penetra-' tion of the mean path of said current with respect to the surface of the earth and produce corresponding variations in the ratio between the values, at two positions adjacent one of said electrodes, and also in the ratio between the values, at two positions adjacent the other of said electrodes, of an electrical variable created by the flow of said current and influenced by said variations in angle of penetration; and determining variations in each of said ratios for the different spacial arrangements of said electrodes. I

2. A method of determining the geological nature and characteristics of the subsurface, which comprises: passing an electric current in a path through the earth between a pair of spaced electrodes having a known spacial arrangement on the surface of the earth; repeating such passage of such an electric current with the electrodes having a different spacial arrangement on the surface of the earth; and determining variations in the ratio of the potential differences existing, during the passage of said current, between two pairs of points located on the surface of the earth adjacent one of said electrodesand so positioned that the respective intervals defined by said pairs of points lie at opposite sides of a plane passing through said one electrode and perpendicular to a straight line passing through said electrodes, when said electrodes have said different spacial arrangements.

3. A method of determining the geological nature and characteristics of-the subsurface, which comprises: maintaining a flow of electric current in a path through the earth between a pair of spaced electrodes, having a known spacial arrangement on the surface of the earth, for a deflnite interval of time greater than one second; and

taking a measurement adjacent at least one of said electrodes which is indicative of the angle of penetration of said current adjacent said lastnamed electrode, at the end of said interval of time and during the flow of said current.

4. In the method of geological surveying in which an electric current is caused to flow in a path through the earth between a pair ofspaced electrodes having a known spacial arrangement on the surface of the earth and in which measurements indicative of the angle of penetration of the current flowing adjacent at least one of said electrodes are taken, successively, during the flow of current between said electrodes at each of a plurality of different spacial arrangements of said electrodes, the steps which comprise: establishing said flow of electric current between said electrodes for each of said plurality of spacial arrangements; maintaining said flow ofcurrent between said electrodes for the same definite interval of time for each of said plurality of spacial arrangements; taking said measurement at the end of said definite interval of time after the establishment of the flow of current between the electrodes at the respective spacial arrangements; and maintaining a definite interval of time between the establishment of the flow of current between the electrodes at any one of said' plurality of spacialarrangements of said electrodes and the establishment of current between said electrodes for the next succeeding spacial arrangement vof said electrodes, said definite time intervals each being greater than one second.

5. An apparatus for use in determining the geologic nature and characteristics of the subsurface, which comprises: a pair of energizing electrodes electrically connected to the surface of the earth and spaced from one another along the surface thereof; a source of electric current connected to said energizing electrodes for passing an energizing current through the earth between said electrodes; and means for measuring the 'arwgms ratio of an electrical variable influenced by the mean path of said energizing current with respect to the surface of the earth, at two'positions adjacent one of said energizing electrodes and at opposite sides of a plane passing through said one electrode and perpendicular to the line joining said electrodes.

6. An apparatus for use in determining the geologic nature and characteristics of the subsurface, which comprises: a pair of energizing electrodes electrically connected to the surface of the earth and spaced from one another along the surface thereof; a source of electric current connected' to said energizing electrodes for passing an energizing current through the earth between said electrodes; and means for determining the ratio of the potential diflerences existing during the passage of said energizing current, between two pairs of spaced points on the surface of the earth adjacent one of said energizing electrodes and at opposite, sides'of a plane passing through said one electrode and perpendicular to a straight line passing through said energizing electrodes.

7. An apparatus for use in determining the geologic nature and characteristics of the subsurface, including means for measuring the ratios of potentials existing at two points with respect to a third point which comprises: a pair of triodeseach having a grid, a cathode, and a plate; a voltage divider connected to the plates of said triodes; an indicating instrument connected in shunt with said voltage divider; a variable tap on said voltage divider; a source of plate potential having one side connected to said variable tap and the other side associated with the cathodes of said triodes; a pair of conductors respectively connecting the grids of said triodes to said two points; and a source of bias potential connected between the cathodes of said triodes and said third point.

8. A method of determining the geological nature and characteristics of the subsurface, which comprises: passing an electric current in a path through the earth between a pair of spaced electrodes having a known spacial arrangement on the surface of the earth; changing the spacial arrangement of said electrodes and passing current therebetween at different spacial arrangements thereof so as to vary the angle of penetration of the mean path of said current with respect to the surface of the earth and produce corresponding variations in the ratio between the values, at two positions adjacent one of said electrodes and located at opposite sides of a plane passing through said one electrode and perpendicular to the line joining said electrodes, of an electrical variable created by the flow of said current andinfluenced by said variations in angle of penetration; and determining variations in said ratio for the difierent spacial arrangements of said electrodes.

9. A method as set forth in claim 8, in which said two positions are located substantially along a straight line passing through said electrodes. and at opposite sides of said one electrode.

JOHN JAY JAKOSKY. 

